1. Field of the Invention
The present invention relates to an adaptive apparatus which performs an adaptive adjustment of vector parameters of a system on a block basis.
2. Description of the Related Art
Nowadays, various adaptive systems are available which have functions for adjusting system parameters in an adaptive manner, such as adaptive control systems, adaptive identification systems, adaptive observation systems and adaptive equalization systems. In general, an adaptive system is a system in which system parameters designed to rule the system performance are adjusted in an adaptive manner in accordance with a variation in the characteristic of the adaptation object and/or the characteristics of the environmental conditions of the object, so as to maintain the operating conditions to optimize the performance of the system.
In order to effect an adaptive adjustment of a system parameter in response to a variation of characteristics, it is necessary that the rate or speed of the adaptive adjustment be higher than that of the change in the characteristic. To comply with such a demand, an adaptive method known as the "block adaptive method" has been used in which the signals used for adjusting parameters are processed on a block basis.
Thus, the principle of the block adaptive method is to process the signals on the block basis. In such a case, the signals are treated as a matrix signal.
In general, the following error equations are utilized to deduce a way of the adjustment of parameters for the block adaptive method. ##EQU1##
In these equations, k represents an integer variable to make functions, employing a factor of time as a discrete variable, using a predetermined sampling time .epsilon.(k) and e (k) respectively represent vector errors of q.times.1 matrixes, Z(k) represents a matrix signal of an available p.times.q matrix, Z.sup.T (k) is a matrix signal of the transposed matrix, .theta. represents a vector parameter of a desirable bounded unknown p.times.1 matrix (vector), .theta. represents a system parameter of a p.times.1 matrix (vector) as an adaptive estimate of .theta., .PSI.(k) represents the parameter error of a p .times.1 represented by .PSI.(k)=.theta.(k)-.theta., and s(k) represents a vector signal of an available q.times.1 matrix (vector) represented by s(k)=Z.sup.T (k).PSI..
In an adaptive system, it is necessary that the vector parameter .theta.(k) is adjusted to satisfy the conditions of the following formulae (3) to (6). ##EQU2##
The formula (3) shows that the vector error .epsilon.(k) is zero at the limit. The formula (4) shows that the system parameter .theta.(k) is always bounded. The formula (5) represents that the amount of correction of the system parameter is 0 at the limit. The formula (6) shows a stricter condition than the formula (5), and means that the adaptively adjusted parameter .theta.(k) takes the desirable value .theta. at the limit.
For the purpose of executing the above-described adjustment, the known adaptive apparatus employ an adjusting method which utilizes the following formula (7) as proposed by G. A. Clark, S. K. Mitra and S. R. Parker: Block implementation of Adaptive Digital Filter, IEEE Trans. Acoustics, Speech and Signal Processing, Vol. ASSP-29, No. 3, pp. 744-752 (1981). EQU .theta.(k)=.theta.(k-1)-.gamma.Z(k) e(k) (7)
In this formula, .gamma. represents an adaptive gain of a fixed scalar referred to as "step size". The formula (7) successively adjusts the system parameter .theta.(k) by using the adaptive gain .gamma., matrix signal Z(k) and the vector error e(k).
In the known method in which the system parameter .theta.(k) is adaptively adjusted in accordance with the formula (7), the performance of the adaptive adjustment is controlled by the adaptive gain .gamma. alone, once the matrix signal Z(k) and the vector error e(k) have become available.
In this case, however, the convergence of the system parameter .theta.(k) is impaired due to the fact that only one adaptive gain, which is a fixed scalar, is used, Thus, the conditions shown by the formulae (3) to (6) can not always be obtained and may fail particularly when the adaptive gain .gamma. is large. In order that the conditions of the formulae (3) to (6) are secured, it is generally necessary to reduce the adaptive gain .gamma. considerably. In such a case, however, the speed of convergence of the system parameter .theta.(k) is seriously decreased, as will be clearly seen from the formula (7).
Conversely, when the adaptive gain is increased to attain a higher convergence speed, the stability of the convergence is often impaired, resulting in a divergence of the system parameter in the worst case.
These problems are ascribed to the fact that a single fixed scalar is used as the adaptive gain.
The basic concept of the adaptive system is to determine the system structure such that the system performance is governed by system parameters, and to adjust the system parameters in an adaptive manner so as to maximize the performance of the system. The performance of the adaptive system, therefore, largely depends on the adaptive apparatus which adjusts the system parameters in adaptive manner. Thus, it has been impossible to construct an adaptive system having superior performance, with the known adaptive apparatus which suffers from the aforementioned problems.